Energy-Momentum Distribution in General Relativity for a Phantom Black Hole Metric

TL;DR

This paper evaluates the energy-momentum distribution of a phantom black hole in General Relativity using Møller and Landau-Lifshitz prescriptions, revealing dependencies on black hole parameters and analyzing various radial limits.

Contribution

It applies energy-momentum definitions to a phantom black hole metric, providing new insights into energy distribution and momentum in such spacetimes.

Findings

Energy distribution depends on mass, phantom constant, and radius.

All calculated momenta are zero.

Analyzes limits as radius approaches zero, infinity, and negative infinity.

Abstract

We use the M{\o}ller and Landau-Lifshitz energy-momentum definitions in General Relativity (GR) to evaluate the energy-momentum distribution of the phantom black hole space-time. The phantom black hole model was applied to the supermassive black hole at the Galactic Centre. We obtain that in both pseudotensorial prescriptions the energy distribution depends on the mass $M$ of the black hole, the phantom constant $p$ and the radial coordinate $r$. Further, all the calculated momenta are found to be zero. The limiting cases $r\rightarrow 0$, $r\rightarrow \infty $ and $r\rightarrow -\infty $ have also been the subject of the study.